Determine the electrical conductivity of open-cell cellular solids based on the characteristics of mesoscale structure

Mesoscale structure characteristics of cellular solids can significantly influence their mechanical behaviors and physical properties (i.e. electrical conductivity in this study). However, there is a lack of accurate and efficient model to describe the relationship between the electrical conductivity of cellular solids and their mesoscale structure characteristics. In this paper, the electrical conductivity of the open-cell cellular solids is studied using mesoscale 3D Voronoi models with geometric parameters obtained from computed tomography statistics of real open-cell foams. The tortuosity is introduced to describe the complexity of internal connecting path and the image-based analysis is used to calculate the tortuosity and electrical conductivity of mesoscale model, which is verified by the finite element method. The results clarify the existing problems in the classic electrical conductivity model derived by Ashby et al. and the correlation between the derivation of electrical conductivity of regular mesoscale model and the analysis of tortuosity is clarified. A new and accurate relationship between relative electrical conductivity and relative density is proposed, in which the constant can be determined by tortuosity without using empirical parameters. Furthermore, it is shown that tortuosity can be used to quantify the different gradient distributions and random structural defects. The results and findings of this study offer a valuable understanding of the role of mesoscale model in the study of mechanical and physical properties of cellular solids, which facilitates the description and design of cellular solids.